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Sum of Two Rational Expressions with Different Denominators - Math

Give an example of a sum of two rational expressions with different denominators, then perform the operation by showing all the steps, including how you found the common denominator. These rational expressions must have a variable in the denominator, such as (3x+1) / (x^2 – 1). Give another example of a sum, ratio, product, or different of two rational expressions for your classmates to solve. Again, the example must have a variable in the denominator. When might you use rational expressions in real life?

Comments for Sum of Two Rational Expressions with Different Denominators - Math

Give an example of a sum of two rational expressions with different denominators, then perform the operation by showing all the steps, including how you found the common denominator. These rational expressions must have a variable in the denominator, such as (3x+1) / (x^2 – 1). Give another example of a sum, ratio, product, or different of two rational expressions for your classmates to solve. Again, the example must have a variable in the denominator. When might you use rational expressions in real life?

Answer:

The technique for adding rational expressions with different denominators is exactly the same procedure as adding fractions with different denominators.

So . . . let’s briefly review the process as it applies to fractions, and then apply it to rational expressions.

1/3 + 2/5

To add these fractions, they must have a common denominator

1/3 + 2/5

= (1/3)*(5/5) + (2/5)*(3/3)

= (1*5)/(3*5) + (2*3)/(5*3)

= 5/15 + 6/15

Both fractions can now be added because they each have the same denominator

5/15 + 6/15

= (5 + 6)/15

= 11/15

Therefore,

1/3 + 2/5 = 11/15

Now, let’s apply this same procedure to the addition of two rational expressions:

Add

(3x + 1) / (x - 1) and (x) / (4x + 1)

= (3x + 1) / (x - 1) + (x) / (4x + 1)

To add these fractions, they must have a common denominator

The new common denominator will be equal to the two existing denominators multiplied together:

(x - 1) * (4x + 1) = 4x² - 3x - 1

Convert the two fractions to the common denominator (x - 1) * (4x + 1)